This volume provides an overview of rationality problems by surveying research from leading experts in the field. Readers will find coverage of rationality problems from both cohomological and algebraic geometry perspectives. Editor(s): Bogomolov, Fedor; Tschinkel, Yuri. Series: Progress in Mathematics. Num Pages: 314 pages, 47 black & white illustrations, 38 black & white tables, biography. BIC Classification: PBG; PBMW. Category: (P) Professional & Vocational. Dimension: 240 x 160 x 24. Weight in Grams: 630. . 2009. Hardback. . . . . Books ship from the US and Ireland.

Bestandsnummer des Verk�ufers V9780817649333

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Bibliografische Details

Titel: Cohomological and Geometric Approaches to Rationality Problems
Verlag: Birkhauser Boston Inc
Erscheinungsjahr: 2009
Sprache: Englisch
ISBN-10: 0817649336
ISBN-13: 9780817649333
Einband: Hardcover
Zustand: New

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Inhaltsangabe

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry.

This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties.

This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems.

Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. B�hning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov

Von der hinteren Coverseite

Rationality problems link algebra to geometry. The difficulties involved depend on the transcendence degree over the ground field, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. These advances have led to many interdisciplinary applications of algebraic geometry.

This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality of moduli spaces of curves, and rational points on algebraic varieties.

This volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems.

I. Bauer

C. B�hning

F. Bogomolov

F. Catanese

I. Cheltsov

N. Hoffmann

S.-J. Hu

M.-C. Kang

L. Katzarkov

B. Kunyavskii

A. Kuznetsov

J. Park

T. Petrov

Yu. G. Prokhorov

A.V. Pukhlikov

Yu. Tschinkel

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